1. Field of the Invention
The invention relates generally to error correction systems and, more particularly, to systems that use selected numbers of redundancy symbols.
2. Background Information
Data stored on magnetic media, such as magnetic disks, are typically stored in encoded form, so that errors in the stored data can possibly be corrected. The errors may occur, for example, because of inter-symbol interference, a defect in the disk, or noise. If more errors are likely, and the system is thus required to correct greater numbers of errors, more error correction information in the form of redundancy symbols is required to be stored on the disk. Some of the trade-offs for including increased error correction information on the disk are the extra time associated with encoding and decoding the data and the complexity of the encoding and decoding systems.
Encoders for encoding data in accordance with cyclic error correction codes (“ECCs”) to produce the redundancy, or ECC, symbols are well known. An encoder that encodes the data using a given ECC manipulates the data symbols in accordance with the corresponding generator polynomial. A conventional encoder that encodes data in accordance with an ECC that produces “j” ECC symbols includes j Galois Field multipliers. The Galois Field multipliers are associated, respectively, with the j coefficients of the corresponding generator polynomial, g(x). The encoder also includes j adders that combine the products associated with a given data symbol with the results of the encoding of the previous data symbol, and j registers that hold the sums produced by the adders. At the end of the encoding, the j registers contain the j ECC symbols.
Alternatively, the data may be encoded to produce the j ECC symbols using a circuit that includes, in addition to the j Galois Field multipliers, registers and adders, a chain of j feedback adders, as discussed in an article by Gerhard Fettweis and Martin Hassner entitled A Combined Reed-Solomon Encoder And Syndrome Generator With Small Hardware Complexity, published by IEEE in 1992. Such a circuit, referred to as a Fettweis-Hassner encoder/syndrome combination circuit, is used in systems in which the same Galois Field multipliers are used for both encoding and syndrome generation. The Fettweis-Hassner encoder/syndrome computation circuit, with its j Galois Field multipliers similarly produces j ECC symbols. However, as discussed in the article, the encoding is associated with a latency that is attributable to the delay through the chain of j feedback adders.
A conventional data processing system uses a selected encoder to encode n-j data symbols in accordance with the generator polynomial g(x) and produce the j ECC symbols that are to be combined with the data into n-symbol ECC code words. When a given data code word is later retrieved from the disk, the system uses the j ECC symbols to correct up to j/2 errors in the code word.
For certain media, however, ECCs that are capable of correcting more or fewer errors may be used to protect the data. For example, the media manufacturing process may produce media of varying quality. The media that meets the most stringent quality standards may require less error protection, and thus, require fewer ECC symbols. In contrast, the media that does not meet the same quality standards requires greater error protection and thus more ECC symbols.
Known prior systems use complex and/or time consuming encoding/decoding systems to produce the code words with different numbers of ECC symbols. One such system includes a plurality of encoders, each associated with a different generator polynomial. A user then selects which encoder to use to produce the required number of ECC symbols. The system may instead use a complicated encoding/decoding scheme in which the user essentially deletes selected ECC symbols after encoding. This system uses a single encoder. However, when the data and the retained ECC symbols are later decoded, the system must use a relatively complex and time consuming error-and-erasure decoding scheme to perform error-only decoding.
If the Fettweis-Hassner encoder/syndrome combination circuit is used, the user may disable certain stages of the circuit, to select corresponding numbers of ECC symbols. The same stages are then used for syndrome generation during decoding. Such a system works well for ECCs that include relatively small numbers of ECC symbols, however, the delay associated with the feedback adder chain effectively prohibits the use of the circuit for codes with relatively large numbers of ECC symbols.
Accordingly, what is needed is a less complex and/or time consuming encoding and decoding system that encodes the data to produce a desired number of ECC symbols, and decodes the data and ECC symbols using error-only decoding.